Highest Common Factor of 986, 346, 384, 54 using Euclid's algorithm
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 986, 346, 384, 54 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 986, 346, 384, 54 is 2 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.
Consider we have numbers 986, 346, 384, 54 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b
Highest common factor (HCF) of 986, 346, 384, 54 is 2.
HCF(986, 346, 384, 54) = 2
HCF of 986, 346, 384, 54 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 986, 346, 384, 54 is 2.
Highest Common Factor of 986,346,384,54 is 2
Step 1: Since 986 > 346, we apply the division lemma to 986 and 346, to get
986 = 346 x 2 + 294
Step 2: Since the reminder 346 ≠ 0, we apply division lemma to 294 and 346, to get
346 = 294 x 1 + 52
Step 3: We consider the new divisor 294 and the new remainder 52, and apply the division lemma to get
294 = 52 x 5 + 34
We consider the new divisor 52 and the new remainder 34,and apply the division lemma to get
52 = 34 x 1 + 18
We consider the new divisor 34 and the new remainder 18,and apply the division lemma to get
34 = 18 x 1 + 16
We consider the new divisor 18 and the new remainder 16,and apply the division lemma to get
18 = 16 x 1 + 2
We consider the new divisor 16 and the new remainder 2,and apply the division lemma to get
16 = 2 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 986 and 346 is 2
Notice that 2 = HCF(16,2) = HCF(18,16) = HCF(34,18) = HCF(52,34) = HCF(294,52) = HCF(346,294) = HCF(986,346) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 384 > 2, we apply the division lemma to 384 and 2, to get
384 = 2 x 192 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 384 is 2
Notice that 2 = HCF(384,2) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 54 > 2, we apply the division lemma to 54 and 2, to get
54 = 2 x 27 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 54 is 2
Notice that 2 = HCF(54,2) .
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Frequently Asked Questions on HCF of 986, 346, 384, 54 using Euclid's Algorithm
1. What is the Euclid division algorithm?
Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.
2. what is the HCF of 986, 346, 384, 54?
Answer: HCF of 986, 346, 384, 54 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 986, 346, 384, 54 using Euclid's Algorithm?
Answer: For arbitrary numbers 986, 346, 384, 54 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
